Are there online spatial data sources similar to software linux package repositories? No.
Are there online collections of free/libre data? Yes, but they are disparate, loosely connected at best.

However there are a few projects I'm aware of which are in a position to eventually become analogous to package repositories:

The already mentioned Open Street Map is probably the most well known / largest contributing community. See the downloading data wiki page for actually getting it.

Esri's arcgis.com has potential. It is hampered by its focus on their own products and that most of the maps are mashups, with the actual data not necessarily available except as WMS services. If more people (organizations) can be persuaded to upload their products as Layer Packages this will be ameliorated. (Layer packages are just 7zip'ped archives of a file geodatabase, an mxd, and ancillary data. With File GDB API anyone will (eventually) be read the data). Performance is somewhat lacking at present and could be improved.

GeoCommons.com by FortiusOne is the one I have the most hope for. It's not software or user group specific as the others are and is designed from the ground up for uploading & downloading data as well as web mapping.

I've tried to create a site a bit like the online repository that you want. My Free GIS data list provides links to a huge amount of data, sorted by category. The sort of data that is available includes the things you were looking for - there are about 3 different datasets which include administrative regions of the US, and at least one dataset for bathymetry of the oceans.

Most of the datasets listed by other answers are also listed on this site.